Method and apparatus for spectrum deconvolution and reshaping

Abstract

A method and apparatus for filter spectrum deconvolution and reshaping include providing a filter output of a spectrum signal and determining the intensity and wavelength of the spectrum signal at each spectral peak. The filter output is characterized as an integral of convolution of a spectrum signal function and a filter function. Transformation are then performed on the filter output to deconvolve and remove the undesirable filter function and add a desirable filter function to reshape the output filter spectrum.

1. A method for filter spectrum deconvolution and reshaping, comprising:
 providing a Fabry-Perot filter output of an input spectrum signal; 
 determining the intensity and wavelength of the spectrum signal at each spectrum peak; 
 characterizing the Fabry-Perot filter output as an integral of convolution of an input spectrum signal function and a Lorentzian filter function; 
 composing a predetermined optimal bandwidth Lorentzian signal and doing a fast Fourier transformation on the Lorentzian function; 
 composing a predetermined optimal bandwidth Gaussian signal and doing a fast Fourier transformation on the Gaussian function; 
 performing fast Fourier transformations on the Fabry-Perot filter output; 
 dividing the results of:
 performing fast Fourier transformations on the Fabry-Perot filter output 
 
 by
 composing a predetermined optimal bandwidth Lorentzian signal and doing a fast Fourier transformation on the Lorentzian function; 
 
 to deconvolve and remove the Lorentzian filter function from the Fabry-Perot filter output; and 
 multiplying the results of:
 dividing the results 
 
 by
 composing a predetermined optimal bandwidth Gaussian signal and doing a fast Fourier transformation on the Gaussian function; 
 
 to add a Gaussian filter function component into the Fabry-Perot filter output; and then 
 doing an inverse fast Fourier transformation on the result of the dividing and the multiplying to finish deconvolving and reshaping the output spectrum signal function. 
 
   
   
     2. The method of  claim 1  wherein providing a Fabry-Perot filter output of an input spectrum signal further comprises measuring a spectrum signal with a tunable Fabry-Perot filter. 
   
   
     3. The method of  claim 1  wherein providing a Fabry-Perot filter output of an input spectrum signal further comprises providing a Fabry-Perot filter output of an optical spectrum signal. 
   
   
     4. The method of  claim 1  wherein providing a Fabry-Perot filter output of an input spectrum signal further comprises providing a Fabry-Perot filter output of a DWDM optical spectrum signal. 
   
   
     5. The method of  claim 1  further comprising repeating the providing, the determining, the characterizing, the composing a predetermined optimal bandwidth Lorentzian signal, the composing a predetermined optimal bandwidth Gaussian signal, the performing, the dividing, the multiplying, and the doing for each wavelength of interest in the spectrum of the spectrum signal to determine corresponding discrete signal powers for each of the respective wavelengths of interest. 
   
   
     6. Apparatus for filter spectrum deconvolution and reshaping, comprising:
 a filter for providing a Fabry-Perot filter output of an input spectrum signal; 
 a detector for determining the intensity and wavelength of the spectrum signal at each spectrum peak; 
 circuitry for characterizing the Fabry-Perot filter output as an integral of convolution of an input spectrum signal function and a Lorentzian filter function; 
 circuitry for composing a predetermined optimal bandwidth Lorentzian signal and doing a fast Fourier transformation on the Lorentzian function; 
 circuitry for composing a predetermined optimal bandwidth Gaussian signal and doing a fast Fourier transformation on the Gaussian function; 
 circuitry for performing fast Fourier transformations on the Fabry-Perot filter output; 
 circuitry for dividing the results of:
 performing fast Fourier transformations on the Fabry-Perot filter output 
 
 by
 composing a predetermined optimal bandwidth Lorentzian signal and doing a fast Fourier transformation on the Lorentzian function; 
 
 to deconvolve and remove the Lorentzian filter function from the Fabry-Perot filter output; and 
 circuitry for multiplying the results of:
 dividing the results 
 
 by
 composing a predetermined optimal bandwidth Gaussian signal and doing a fast Fourier transformation on the Gaussian function; 
 
 to add a Gaussian filter function component into the Fabry-Perot filter output; 
 circuitry for dividing the result of:
 multiplying the results 
 
 by
 composing a Lorentzian signal and doing a fast Fourier transformation on the Lorentzian signal, 
 
 to deconvolve and remove the Lorentzian filter function from the Fabry-Perot filter output; and 
 circuitry for doing an inverse fast Fourier transformation on the result of the dividing and the multiplying to finish deconvolving and reshaping the output spectrum signal function. 
 
   
   
     7. The apparatus of  claim 6  wherein the Fabry-Perot filter further comprises a tunable Fabry-Perot filter. 
   
   
     8. The apparatus of  claim 6  wherein the Fabry-Perot filter further comprises a Fabry-Perot filter for providing a filter output of an optical spectrum signal. 
   
   
     9. The apparatus of  claim 6  wherein the Fabry-Perot filter further comprises a Fabry-Perot filter for providing a filter output of a DWDM optical spectrum signal. 
   
   
     10. The apparatus of  claim 6  further comprising circuitry for repeating the providing, the determining, the characterizing, the composing a predetermined optimal bandwidth Lorentzian signal, the composing a predetermined optimal bandwidth Gaussian signal, the performing, the dividing, the multiplying, and the doing for each wavelength of interest in the spectrum of the spectrum signal to determine corresponding discrete signal powers for each of the respective wavelengths of interest.